Finite Group Databasebeta

← #21455063

Subgroups — #21455063

Order 7808.

758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#11758224C211yesmaximal, characteristic, complemented
2C2×#14519810C211yesmaximal, characteristic, complemented
3C2×#14519803C211yesmaximal, characteristic, complemented
4#16840274C211yesmaximal, characteristic, complemented
5#16839925C214yesmaximal, complemented
6#16839908C214yesmaximal, complemented
7#16839770C211yesmaximal, characteristic, complemented
8#16839725C211yesmaximal, characteristic, complemented
9C61×#418C211yesmaximal, characteristic, complemented
10C2×#11758222C2211yescharacteristic
11C2×#11758224—24no—
12C2×#11758224—22no—
13C2×#11758224—24no—
14C2×#11758224C2214yes—
15C22×Dic122C2211yescharacteristic
16C22×C22⋊D61—21no—
17C23×Dic61—21no—
18C22×C4×D61C2211yescharacteristic
19#14519810—24no—
20#14519803—24no—
21C2×Dic244C2212yescomplemented
22C2×#11758190C2212yescomplemented
23C2×#11758200C2212yescomplemented
24C2×#11758199C2212yescomplemented
25C2×#11758194C2211yescharacteristic
26#14519761—21no—
27#14519757C2212yescomplemented
28#14519752C2212yescomplemented
29#14519747—21no—
30C4×D244—22no—
31#14519700C2214yescomplemented
32#14519689C2214yescomplemented
33C22×D4×C61C2211yescharacteristic
34C2×M16×C61C2211yescharacteristic
35#117×C61C2211yescharacteristic
36#102×C61C2214yescomplemented
37C24×C61—21no—
38C23×D61D411yescharacteristic
39C2×D4×C61—21no—
40C2×D4×C61—22no—
41C2×D4×C61D414yescomplemented
42C2×D4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C2×C22⋊D61—28no—
45C2×C22⋊D61—24no—
46C2×C22⋊D61—21no—
47C22×Dic61—28no—
48C22×Dic61—21no—
49C22×Dic61—24no—
50C22×Dic61D411yescharacteristic
51#11758224—216no—
52#11758224—28no—
53#11758224—28no—
54#11758222—22no—
55#11758222—22no—
56C2×D244—22no—
57C2×D244C2311yescharacteristic
58C2×C4×D61—22no—
59C2×C4×D61—22no—
60C2×C4×D61—21no—
61C2×C4×D61D412yes—
62C2×C4×D61C2312yes—
63C2×Dic122—21no—
64C2×Dic122—22no—
65C2×Dic122D414yescomplemented
66C2×Dic122C2311yescharacteristic
67C2×Dic122C2312yes—
68M16×C61—22no—
69C2×C8×C61C2312yes—
70C4⋊C4×C61C2312yes—
71C22⋊C4×C61—21no—
72C42×C61—21no—
73#11758200—24no—
74#11758199—24no—
75#11758198—22no—
76#11758198—22no—
77C4⋊Dic61—22no—
78#11758194—22no—
79C2×#92418C2312yes—
80Dic244—24no—
81#11758190—24no—
82C23×C61—24no—
83C23×C61—22no—
84C23×C61—44no—
85C23×C61C2×D411yescharacteristic
86C22×D61—22no—
87C22×D61—21no—
88C22×D61—42no—
89C22×D61C2×D412yes—
90D4×C61—24no—
91D4×C61—22no—
92D4×C61C2×D414yes—
93C2×C4×C61—22no—
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2×D412yes—
96C2×C4×C61C2×D412yes—
97C2×C4×C61C2411yescharacteristic
98C22⋊D61—216no—
99C22⋊D61—42no—
100C2×Dic61—216no—
101C2×Dic61—24no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—21no—
105C2×Dic61C2×D412yes—
106D244—21no—
107D244—21no—
108D244—44no—
109C4×D61—24no—
110C4×D61—22no—
111C4×D61—22no—
112C4×D61—42no—
113Dic122—24no—
114Dic122—22no—
115Dic122—21no—
116Dic122—21no—
117Dic122C2×D414yes—
118C8×C61—22no—
119#92418—22no—
120C22×C61—22no—
121C22×C61—24no—
122C22×C61—48no—
123C22×C61—44no—
124C22×C61#12012yes—
125C22×C61C22×D411yescharacteristic
126C2×D61—22no—
127C2×D61—22no—
128C2×D61—22no—
129C2×D61—44no—
130C2×D61—41no—
131C2×D61—42no—
132C4×C61—42no—
133C4×C61#12012yes—
134C4×C61C22×D411yescharacteristic
135C4×C61C22×D411yescharacteristic
136Dic61—24no—
137Dic61—22no—
138Dic61—41no—
139#3005—611nomaximal, Sylow
140C2×C61—22no—
141C2×C61—44no—
142C2×C61C2×#12011yescharacteristic
143C2×C61#57512yes—
144D61—42no—
145D61—81no—
146C22×#41—611no—
147C2×#137—611no—
148C2×AGL(1,ℤ/8)—611no—
149#525—611no—
150#452—614no—
151#449—614no—
152#419—611no—
153#418D6111yescharacteristic, complemented
154#407—611no—
155C61#300511yescharacteristic, complemented, Sylow
156C2×#41—614no—
157C2×#41—611no—
158C2×#41—1222no—
159C2×#41—1224no—
160C2×#41—1224no—
161C22×Q8—611no—
162C22×D4—1221no—
163C22×D4C2×D6111yescharacteristic
164C23×C4—611no—
165C23×C4—1221no—
166#137—1224no—
167AGL(1,ℤ/8)—1224no—
168C2×Q16—612no—
169C2×SD16—612no—
170C2×SD16—612no—
171C2×D8—612no—
172C2×M16—611no—
173C2×M16C2×D6111yescharacteristic
174#123—1221no—
175C22⋊Q8—612no—
176#121—612no—
177#120—1221no—
178C4×D4—1222no—
179#117C2×D6111yescharacteristic
180#103—614no—
181#102C2×D6114yescomplemented
182C22⋊C8—614no—
183C24—21no—
184C24—611no—
185#41—1228no—
186#41—12216no—
187#41—1228no—
188#41—1222no—
189#41—1222no—
190C2×Q8—614no—
191C2×Q8—612no—
192C2×Q8—611no—
193C2×Q8—1222no—
194C2×Q8—1221no—
195C2×D4—22no—
196C2×D4—21no—
197C2×D4—611no—
198C2×D4—1222no—
199C2×D4—1224no—
200C2×D4—1228no—
201C2×D4—1221no—
202C2×D4D24414yescomplemented
203C2×D4C22×D6112yes—
204C22×C4—611no—
205C22×C4—612no—
206C22×C4—612no—
207C22×C4—1224no—
208C22×C4—1228no—
209C22×C4—1221no—
210C22×C4—1222no—
211C22×C4—1222no—
212C22×C4—1221no—
213C22×C4C22×D6111yescharacteristic
214Q16—1224no—
215SD16—1224no—
216SD16—1224no—
217D8—1224no—
218M16—22no—
219M16—1222no—
220C2×C8—612no—
221C2×C8C22×D6112yes—
222C4⋊C4—1222no—
223C4⋊C4C22×D6112yes—
224C22⋊C4—21no—
225C22⋊C4—1222no—
226C22⋊C4—1222no—
227C42—21no—
228C23—22no—
229C23—24no—
230C23—44no—
231C23—612no—
232C23—1222no—
233C23—1221no—
234C23—2442no—
235C23D4×D6111yescharacteristic
236Q8—614no—
237Q8—1222no—
238Q8—1224no—
239Q8—1221no—
240Q8—1221no—
241D4—22no—
242D4—24no—
243D4—12216no—
244D4—1221no—
245D4—1221no—
246D4—2444no—
247D4—2442no—
248D4C2×D24414yes—
249C2×C4—22no—
250C2×C4—612no—
251C2×C4—12216no—
252C2×C4—1222no—
253C2×C4—1222no—
254C2×C4—1224no—
255C2×C4—1222no—
256C2×C4—1222no—
257C2×C4—1224no—
258C2×C4—1221no—
259C2×C4—2442no—
260C2×C4C2×D24412yes—
261C2×C4D4×D6112yes—
262C2×C4D4×D6111yescharacteristic
263C2×C4C23×D6111yescharacteristic
264C8—22no—
265C8—1222no—
266C22—22no—
267C22—24no—
268C22—48no—
269C22—44no—
270C22—1222no—
271C22—1222no—
272C22—1222no—
273C22—2444no—
274C22—2441no—
275C22—2442no—
276C22#1451974712yes—
277C22C2×D4×D6111yescharacteristic
278C4—42no—
279C4—1222no—
280C4—1224no—
281C4—2441no—
282C4#1451974712yes—
283C4C2×D4×D6111yescharacteristic
284C4C22×D24411yescharacteristic
285C2—22no—
286C2—44no—
287C2—4881no—
288C2—2442no—
289C2C2×#1451974711yescharacteristic
290C2#1684055812yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#418C2
socleC22×C61C22×D4
hypercenter#418D61
hypocenterC61#3005
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#11758224C2semidirect
2. C2×#14519810C2semidirect
3. C2×#14519803C2semidirect
4. #16840274C2semidirect
5. #16839925C2semidirect
6. #16839908C2semidirect
7. #16839770C2semidirect
8. #16839725C2semidirect
9. C61×#418C2semidirect
21. C2×Dic244C22semidirect
22. C2×#11758190C22semidirect
23. C2×#11758200C22semidirect
24. C2×#11758199C22semidirect
27. #14519757C22semidirect
28. #14519752C22semidirect
31. #14519700C22semidirect
32. #14519689C22semidirect
36. #102×C61C22semidirect
41. C2×D4×C61D4semidirect
65. C2×Dic122D4semidirect
153. #418D61semidirect
155. C61#3005semidirect
181. #102C2×D61semidirect
202. C2×D4D244semidirect